Suppose the population distribution of BMI among teenage girls is right-skewed.

Question

Suppose the population distribution of BMI among teenage girls is right-skewed. If you took a sample of 20 teenage girls, would the sampling distribution of average BMI follow an approximately normal distribution? a. Yes, because the shape of the population distribution does not affect the shape of the sampling distribution b. No, because the underlying population distribution is right-skewed, so no matter the sample size the sampling distribution cannot be normal. c. Yes, because we have more than ten observations, and according to the Central Limit Theorem that is large enough for the sampling distribution to be close to bell-shaped even though the underlying population distribution is right-skewed d. No, because the underlying population distribution is right-skewed and we have less than 30 observations, which is the cutoff used for the Central Limit Theorem to apply.

Explanation / Answer

If the underlying population is skewed then to apply central limit theorem, we atleast need 30 observations. Here the population is right skewed and we have less than 30 size of sample.

So,

Option D is correct.

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